derivative y=(5x^2-6x)^{-2}

解

導関数

y = (5 x^{2} - 6 x)^{- 2}

- \frac{2 ( 10 x - 6 )}{( 5 x ^{2} - 6 x ) ^{3}}

解答ステップ

\frac{d}{d x} ((5 x^{2} - 6 x)^{- 2})

連鎖法則を適用:

- \frac{2}{( 5 x ^{2} - 6 x ) ^{3}} \frac{d}{d x} (5 x^{2} - 6 x)

= - \frac{2}{( 5 x ^{2} - 6 x ) ^{3}} \frac{d}{d x} (5 x^{2} - 6 x)

\frac{d}{d x} (5 x^{2} - 6 x) = 10 x - 6

= - \frac{2}{( 5 x ^{2} - 6 x ) ^{3}} (10 x - 6)

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= - \frac{2 ( 10 x - 6 )}{( 5 x ^{2} - 6 x ) ^{3}}